Speaking to reporters in New York City after dining with Trump Tuesday night, Romney, the 2012 GOP presidential nominee, said the two discussed world affairs during their "enlightening" conversations, but he did not say whether he was offered or discussed the Cabinet position.

For the majority of his remarks, Romney commended the president-elect's growing Cabinet and transition efforts.

"I have to tell you, I've been impressed with what I've seen in the transition. The people he's selected as members of his Cabinet are solid, effective, capable people," Romney said, naming off several of Trump's selections.

"I think you're going to see America continue to lead the world in this century, and what I've seen through these discussions I've had with President-elect Trump, as well as what we've seen in his speech the night of his victory, as well as people he's selected as part of his transition, all of those combined give me increasing hope that President-elect Trump is the very man that can lead us to that better future," Romney said.

He added: "I happen to think America's best days are ahead of us."

Romney also applauded Trump's victory, remarking: "By the way, it's not easy winning. I know that myself. He did something I tried to do and was unsuccessful in."

Romney, who is reportedly at the top of the list to be the nation's chief diplomat under the Trump administration, was one of Trump's harshest GOP critics.

Trump has faced backlash from supporters and advisers for considering Romney to service in his administration.

Others reportedly under consideration for the job are former New York City Mayor Rudy Giuliani, former CIA Director David Petraeus and Tennessee Sen. Bob Corker.

When asked by reporters at Trump Tower if Romney would be nominated for the job, Trump replied: "Well, we're gonna see what happens."

Top Trump adviser Kellyanne Conway told reporters Tuesday night the transition team will make a Cabinet announcement at 6:30 a.m. Wednesday, though she did not elaborate.